To me, it is a matter of how close a person is to me. Friends know, acquaintances do not. However, the level of what I divulge does not only pertain to my relationship proclivities; I am also unlikely to divulge my political, philosophical, and ideas on religion to acquaintances either.
As I do not require validation of my relationships from external sources, I do not feel the need to shout it from the rooftops. That said, if someone were to ask me point blank, I would say that I am in an open relationship and leave it at that. If pressed further, I would explain my philosophy.